Subgroups — C₁₇×#2557 #14525563

Order 2176.

582 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#393	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#392	C₂	1	1	yes	maximal, characteristic
7	C₁₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#388	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#386	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂²⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₁₇	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₁₇	C₂²	1	1	yes	characteristic
22	C₁₇×#124	—	2	4	no	—
23	C₁₇×#123	—	2	4	no	—
24	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
42	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
43	C₁₇×#95	C₂²	1	1	yes	characteristic
44	C₁₇×#95	C₂²	1	1	yes	characteristic
45	C₁₇×#95	C₂²	1	1	yes	characteristic
46	C₁₇×#95	C₂²	1	1	yes	characteristic
47	C₁₇×#95	C₂²	1	1	yes	characteristic
48	C₁₇×#95	C₂²	1	1	yes	characteristic
49	C₁₇×#95	C₂²	1	1	yes	characteristic
50	C₁₇×#95	C₂²	1	1	yes	characteristic
51	C₁₇×#95	C₂²	1	1	yes	characteristic
52	C₁₇×#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
54	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
55	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
56	C₂×Q₈×C₁₇	—	2	2	no	—
57	C₂×Q₈×C₁₇	—	2	2	no	—
58	C₂×Q₈×C₁₇	—	4	1	no	—
59	C₂×D₄×C₁₇	—	2	2	no	—
60	C₂×D₄×C₁₇	—	2	2	no	—
61	C₂×D₄×C₁₇	—	2	2	no	—
62	C₂×D₄×C₁₇	—	2	2	no	—
63	C₂×D₄×C₁₇	—	2	2	no	—
64	C₂×D₄×C₁₇	—	2	2	no	—
65	C₂×D₄×C₁₇	—	4	1	no	—
66	C₂×D₄×C₁₇	—	4	1	no	—
67	C₂×D₄×C₁₇	—	4	1	no	—
68	C₂²×C₄×C₁₇	—	2	2	no	—
69	C₂²×C₄×C₁₇	—	2	2	no	—
70	C₂²×C₄×C₁₇	—	2	2	no	—
71	C₂²×C₄×C₁₇	—	4	1	no	—
72	C₂²×C₄×C₁₇	—	4	1	no	—
73	C₂²×C₄×C₁₇	—	4	1	no	—
74	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₁₇	—	2	2	no	—
87	C₄⋊C₄×C₁₇	—	2	2	no	—
88	C₄⋊C₄×C₁₇	—	2	2	no	—
89	C₂²⋊C₄×C₁₇	—	2	2	no	—
90	C₂²⋊C₄×C₁₇	—	2	2	no	—
91	C₂²⋊C₄×C₁₇	—	2	2	no	—
92	C₂²⋊C₄×C₁₇	—	2	2	no	—
93	C₂²⋊C₄×C₁₇	—	2	2	no	—
94	C₂²⋊C₄×C₁₇	—	2	2	no	—
95	C₂²⋊C₄×C₁₇	—	2	2	no	—
96	C₂²⋊C₄×C₁₇	—	2	2	no	—
97	C₂²⋊C₄×C₁₇	—	2	2	no	—
98	C₂²⋊C₄×C₁₇	—	4	1	no	—
99	C₂²⋊C₄×C₁₇	—	4	1	no	—
100	C₂²⋊C₄×C₁₇	—	4	1	no	—
101	C₂²⋊C₄×C₁₇	D₄	1	4	yes	complemented
102	C₄²×C₁₇	—	2	2	no	—
103	C₄²×C₁₇	—	4	1	no	—
104	C₄²×C₁₇	—	4	1	no	—
105	C₂³×C₁₇	—	2	1	no	—
106	C₂³×C₁₇	—	2	1	no	—
107	C₂³×C₁₇	—	2	1	no	—
108	C₂³×C₁₇	—	2	1	no	—
109	C₂³×C₁₇	—	2	1	no	—
110	C₂³×C₁₇	—	2	1	no	—
111	C₂³×C₁₇	—	2	1	no	—
112	C₂³×C₁₇	—	2	1	no	—
113	C₂³×C₁₇	—	2	1	no	—
114	C₂³×C₁₇	—	2	1	no	—
115	C₂³×C₁₇	—	2	1	no	—
116	C₂³×C₁₇	—	2	1	no	—
117	C₂³×C₁₇	—	2	1	no	—
118	C₂³×C₁₇	—	2	1	no	—
119	C₂³×C₁₇	—	2	1	no	—
120	C₂³×C₁₇	—	2	1	no	—
121	C₂³×C₁₇	—	2	1	no	—
122	C₂³×C₁₇	—	2	1	no	—
123	C₂³×C₁₇	—	2	1	no	—
124	C₂³×C₁₇	C₂×D₄	1	2	yes	—
125	C₂³×C₁₇	#41	1	2	yes	—
126	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
127	Q₈×C₁₇	—	4	4	no	—
128	D₄×C₁₇	—	4	4	no	—
129	D₄×C₁₇	—	4	4	no	—
130	D₄×C₁₇	—	4	4	no	—
131	C₂×C₄×C₁₇	—	2	1	no	—
132	C₂×C₄×C₁₇	—	2	1	no	—
133	C₂×C₄×C₁₇	—	2	1	no	—
134	C₂×C₄×C₁₇	—	2	1	no	—
135	C₂×C₄×C₁₇	—	2	1	no	—
136	C₂×C₄×C₁₇	—	2	1	no	—
137	C₂×C₄×C₁₇	—	2	1	no	—
138	C₂×C₄×C₁₇	—	2	1	no	—
139	C₂×C₄×C₁₇	—	2	1	no	—
140	C₂×C₄×C₁₇	—	2	1	no	—
141	C₂×C₄×C₁₇	—	2	1	no	—
142	C₂×C₄×C₁₇	—	2	1	no	—
143	C₂×C₄×C₁₇	—	2	1	no	—
144	C₂×C₄×C₁₇	—	2	1	no	—
145	C₂×C₄×C₁₇	—	2	1	no	—
146	C₂×C₄×C₁₇	—	2	1	no	—
147	C₂×C₄×C₁₇	—	2	1	no	—
148	C₂×C₄×C₁₇	—	2	1	no	—
149	C₂×C₄×C₁₇	—	2	1	no	—
150	C₂×C₄×C₁₇	—	2	1	no	—
151	C₂×C₄×C₁₇	—	2	1	no	—
152	C₂×C₄×C₁₇	—	2	1	no	—
153	C₂×C₄×C₁₇	—	2	1	no	—
154	C₂×C₄×C₁₇	—	2	1	no	—
155	C₂×C₄×C₁₇	—	2	1	no	—
156	C₂×C₄×C₁₇	—	2	1	no	—
157	C₂×C₄×C₁₇	—	2	1	no	—
158	C₂×C₄×C₁₇	—	2	1	no	—
159	C₂×C₄×C₁₇	—	2	1	no	—
160	C₂×C₄×C₁₇	—	2	1	no	—
161	C₂×C₄×C₁₇	—	2	1	no	—
162	C₂×C₄×C₁₇	—	4	4	no	—
163	C₂×C₄×C₁₇	—	4	4	no	—
164	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
165	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
166	C₂×C₄×C₁₇	#41	1	2	yes	—
167	C₂×C₄×C₁₇	#41	1	2	yes	—
168	C₂×C₄×C₁₇	#41	1	2	yes	—
169	#2557	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₁₇	—	2	2	no	—
171	C₂²×C₁₇	—	2	2	no	—
172	C₂²×C₁₇	—	2	2	no	—
173	C₂²×C₁₇	—	2	2	no	—
174	C₂²×C₁₇	—	2	2	no	—
175	C₂²×C₁₇	—	2	2	no	—
176	C₂²×C₁₇	—	4	1	no	—
177	C₂²×C₁₇	—	4	1	no	—
178	C₂²×C₁₇	—	4	1	no	—
179	C₂²×C₁₇	—	4	1	no	—
180	C₂²×C₁₇	—	4	1	no	—
181	C₂²×C₁₇	—	4	1	no	—
182	C₂²×C₁₇	—	4	1	no	—
183	C₂²×C₁₇	—	4	1	no	—
184	C₂²×C₁₇	—	4	1	no	—
185	C₂²×C₁₇	—	4	1	no	—
186	C₂²×C₁₇	—	4	1	no	—
187	C₂²×C₁₇	—	4	1	no	—
188	C₂²×C₁₇	—	4	1	no	—
189	C₂²×C₁₇	—	4	1	no	—
190	C₂²×C₁₇	—	4	1	no	—
191	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
192	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
193	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
194	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
195	C₂²×C₁₇	C₂×#41	1	1	yes	characteristic
196	C₂²×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂²×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
198	C₄×C₁₇	—	2	2	no	—
199	C₄×C₁₇	—	2	2	no	—
200	C₄×C₁₇	—	2	2	no	—
201	C₄×C₁₇	—	2	2	no	—
202	C₄×C₁₇	—	2	2	no	—
203	C₄×C₁₇	—	4	1	no	—
204	C₄×C₁₇	—	4	1	no	—
205	C₄×C₁₇	—	4	1	no	—
206	C₄×C₁₇	—	4	1	no	—
207	C₄×C₁₇	—	4	1	no	—
208	C₄×C₁₇	—	4	1	no	—
209	C₄×C₁₇	—	4	1	no	—
210	C₂×#124	C₂×C₁₇	1	1	yes	characteristic, complemented
211	C₂×#123	C₂×C₁₇	1	1	yes	characteristic, complemented
212	#397	C₂×C₁₇	1	1	yes	characteristic, complemented
213	#397	C₂×C₁₇	1	1	yes	characteristic, complemented
214	#393	C₂×C₁₇	1	1	yes	characteristic, complemented
215	#392	C₂×C₁₇	1	1	yes	characteristic
216	#391	C₂×C₁₇	1	1	yes	characteristic, complemented
217	#390	C₂×C₁₇	1	1	yes	characteristic, complemented
218	#388	C₂×C₁₇	1	1	yes	characteristic, complemented
219	#387	C₂×C₁₇	1	1	yes	characteristic, complemented
220	#386	C₂×C₁₇	1	1	yes	characteristic, complemented
221	#386	C₂×C₁₇	1	1	yes	characteristic, complemented
222	#386	C₂×C₁₇	1	1	yes	characteristic, complemented
223	C₄×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
224	C₄×C₂²⋊C₄	C₂×C₁₇	1	1	yes	characteristic, complemented
225	C₂×C₁₇	—	4	2	no	—
226	C₂×C₁₇	—	4	2	no	—
227	C₂×C₁₇	—	8	1	no	—
228	C₂×C₁₇	#529	1	1	yes	characteristic
229	C₂×C₁₇	#532	1	1	yes	characteristic
230	C₂×C₁₇	#538	1	1	yes	characteristic
231	C₂×C₁₇	#546	1	1	yes	characteristic
232	C₂×C₁₇	#546	1	1	yes	characteristic
233	C₂×C₁₇	#551	1	1	yes	characteristic
234	C₂×C₁₇	#559	1	1	yes	characteristic
235	C₂²×Q₈	C₂²×C₁₇	1	1	yes	characteristic
236	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
237	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
238	C₂²×D₄	C₂²×C₁₇	1	1	yes	characteristic
239	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²×C₁₇	1	1	yes	characteristic
241	#124	—	2	4	no	—
242	#123	—	2	4	no	—
243	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
259	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
262	#95	C₂²×C₁₇	1	1	yes	characteristic
263	#95	C₂²×C₁₇	1	1	yes	characteristic
264	#95	C₂²×C₁₇	1	1	yes	characteristic
265	#95	C₂²×C₁₇	1	1	yes	characteristic
266	#95	C₂²×C₁₇	1	1	yes	characteristic
267	#95	C₂²×C₁₇	1	1	yes	characteristic
268	#95	C₂²×C₁₇	1	1	yes	characteristic
269	#95	C₂²×C₁₇	1	1	yes	characteristic
270	#95	C₂²×C₁₇	1	1	yes	characteristic
271	#95	C₂²×C₁₇	1	1	yes	characteristic
272	C₁₇	#2557	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
274	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
275	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
298	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
299	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
303	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
304	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
305	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	D₄×C₁₇	1	4	yes	complemented
322	C₄²	—	2	2	no	—
323	C₄²	—	4	1	no	—
324	C₄²	—	4	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	C₂×D₄×C₁₇	1	2	yes	—
345	C₂³	#41×C₁₇	1	2	yes	—
346	C₂³	C₂⁴×C₁₇	1	1	yes	characteristic
347	Q₈	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	4	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	C₂×D₄×C₁₇	1	2	yes	—
385	C₂×C₄	C₂×D₄×C₁₇	1	2	yes	—
386	C₂×C₄	#41×C₁₇	1	2	yes	—
387	C₂×C₄	#41×C₁₇	1	2	yes	—
388	C₂×C₄	#41×C₁₇	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂²×D₄×C₁₇	1	1	yes	characteristic
411	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
412	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
413	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
414	C₂²	C₂×#41×C₁₇	1	1	yes	characteristic
415	C₂²	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	1	no	—
432	C₂	C₁₇×#529	1	1	yes	characteristic
433	C₂	C₁₇×#532	1	1	yes	characteristic
434	C₂	C₁₇×#538	1	1	yes	characteristic
435	C₂	C₁₇×#546	1	1	yes	characteristic
436	C₂	C₁₇×#546	1	1	yes	characteristic
437	C₂	C₁₇×#551	1	1	yes	characteristic
438	C₂	C₁₇×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₇
prime radical	C₁₇×#392	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₇×#124	C₂	semidirect
2. C₂×C₁₇×#123	C₂	semidirect
3. C₁₇×#397	C₂	semidirect
4. C₁₇×#397	C₂	semidirect
5. C₁₇×#393	C₂	semidirect
7. C₁₇×#391	C₂	semidirect
8. C₁₇×#390	C₂	semidirect
9. C₁₇×#388	C₂	semidirect
10. C₁₇×#387	C₂	semidirect
11. C₁₇×#386	C₂	semidirect
12. C₁₇×#386	C₂	semidirect
13. C₁₇×#386	C₂	semidirect
14. C₄×C₂²⋊C₄×C₁₇	C₂	semidirect
15. C₄×C₂²⋊C₄×C₁₇	C₂	semidirect
101. C₂²⋊C₄×C₁₇	D₄	semidirect
169. #2557	C₁₇	direct (N × H)
210. C₂×#124	C₂×C₁₇	semidirect
211. C₂×#123	C₂×C₁₇	semidirect
212. #397	C₂×C₁₇	semidirect
213. #397	C₂×C₁₇	semidirect
214. #393	C₂×C₁₇	semidirect
216. #391	C₂×C₁₇	semidirect
217. #390	C₂×C₁₇	semidirect
218. #388	C₂×C₁₇	semidirect
219. #387	C₂×C₁₇	semidirect
220. #386	C₂×C₁₇	semidirect
221. #386	C₂×C₁₇	semidirect
222. #386	C₂×C₁₇	semidirect
223. C₄×C₂²⋊C₄	C₂×C₁₇	semidirect
224. C₄×C₂²⋊C₄	C₂×C₁₇	semidirect
272. C₁₇	#2557	direct (N × H)
321. C₂²⋊C₄	D₄×C₁₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₇×#124	2
C₂×C₁₇×#123	2
C₁₇×#397	2
C₁₇×#393	2
C₁₇×#392	2
C₁₇×#391	2
C₁₇×#390	2
C₁₇×#388	2
C₁₇×#387	2
C₁₇×#386	2
C₄×C₂²⋊C₄×C₁₇	2
#2557	17

Subgroups — C17×#2557 #14525563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#2557 #14525563